The England international went down under a tackle from Liverpool centre-back Daniel Agger during the first half of his country's friendly against Denmark but went on to play almost an hour of what became a 1-0 win at Wembley.
The midfielder had thought that the pain in his foot was "just a bruise" but is now facing a race to be fit for the World Cup this summer.
"[Wilshere] can only be very down in this situation, he will go away for a few days," Wenger told reporters.
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Wilshere has had more than his fair share of injuries to his foot and ankle over the years but the Gunners boss observed that the latest setback has not affected a previously damaged part. "It is [a setback], yes," he continued, "but it is an accident on a good ankle.
Asked if he had taken exception to Agger's challenge, Wenger replied: "The tackle was strong but I think he wanted to go for the ball, yes."
The 64-year-old was also quizzed on the England medical team's handling of the knock, having sent Wilshere back onto the pitch following treatment, but argued: "At some stage it is the player who gives you the indication. It is the pain of the player that gives you the indication and you trust always the player.
"Sometimes you give him a few minutes - when a guy has been touched like that you give him a few minutes to tell you how he feels and if there's no pain. We are not at the point where we can make an instant check-up with an X-ray to see how big the damage is so most of the time it is the indication of the player to tell you if he can go on or not."
There was good news for the Frenchman, though, who indicated that Aaron Ramsey and Kim Kallstrom could be available for selection as early as the north London derby on March 16, though Laurent Koscielny is a doubt for the FA Cup quarter-final clash with Everton on Saturday.
He added: "We have a little doubt about Koscielny [but] everyone else came back in a good shape."